An Event-Based Framework for Turbulence

Abstract: Traditionally, turbulence research has relied on spectral analysis, linking Fourier wavenumbers or frequencies to eddy length or time scales. This presentation introduces an event-based approach as a novel alternative to spectral methods, addressing three fundamental problems in wall turbulence. Firstly, it focuses on identifying coherent structures within the flow using single-point time series measurements. Secondly, it explores the scales associated with intermittency in wall-bounded turbulence. Thirdly, it quantifies small-scale anisotropy in wall-bounded turbulent flows. To achieve these objectives, innovative time-series analysis techniques are developed. For the first objective, the concept of persistence times is introduced and generalized by the level-crossing method, enabling the objective identification of turbulent time series features related to coherent structures without predefining arbitrary thresholds. For the second and third objectives, a scale-dependent event framework is proposed, viewing the turbulent time series as a sequence of events with finite size and duration across multiple flow scales. Additionally, a network theory-based approach is introduced to further characterize coherent structures. This approach reaffirms the path dependency of nonlinear complex systems like turbulence and generalizes these findings to other non-equilibrium systems.